Blow-Up Solution of Modified-Logistic-Diffusion Equation

Abstract

Modified-Logistic-Diffusion Equation ut=Duxx+u|1-u| with Neumann boundary condition has a global solution, if the given initial condition ψ satisfies ψ(x)≤1, for all x∈[0,1]. Other initial conditions can lead to another type of solutions; i.e., an initial condition that satifies ∫01ψ(x)dx>1 will cause the solution to blow up in a finite time. Another initial condition will result in another kind of solution, which depends on the diffusion coefficient D. In this paper, we obtained the lower bound of D, so that the solution of Modified-Logistic-Diffusion Equation with a given initial condition will have a global solution.